Neil Mellor gave a strong performance in front of watching boss, Rafael Benitez. The Liverpool striker was influential up front, creating a series of chances and sending a header inches wide in the first half.
But the opportunities were not converted and a well struck free-kick from Boznar shot under the wall and past Patrice Luzi into the net, giving the Toffeemen the victory.
Liverpool Reserve team manager, Hughie McAuley, said: "It was a disappointing night for us and when you lose to your nearest rivals it makes it even more disappointing."
"I don't think Everton deserved to win the game as we had three or four good chances and didn't score," he added.